Human Calculator

November 29th, 2018 at 9:04:22 PM permalink
Pacomartin
Member since: Oct 24, 2012
Threads: 869
Posts: 10320
Below is a table of perfect cubes from 1 to a million. If someone gives you one of these numbers at random, can you calculate the cube root in your head?


1 1,331 9,261 29,791 68,921 132,651 226,981 357,911 531,441 753,571
8 1,728 10,648 32,768 74,088 140,608 238,328 373,248 551,368 778,688
27 2,197 12,167 35,937 79,507 148,877 250,047 389,017 571,787 804,357
64 2,744 13,824 39,304 85,184 157,464 262,144 405,224 592,704 830,584
125 3,375 15,625 42,875 91,125 166,375 274,625 421,875 614,125 857,375
216 4,096 17,576 46,656 97,336 175,616 287,496 438,976 636,056 884,736
343 4,913 19,683 50,653 103,823 185,193 300,763 456,533 658,503 912,673
512 5,832 21,952 54,872 110,592 195,112 314,432 474,552 681,472 941,192
729 6,859 24,389 59,319 117,649 205,379 328,509 493,039 704,969 970,299
1,000 8,000 27,000 64,000 125,000 216,000 343,000 512,000 729,000 1,000,000


For example, what is the cube root of 681,472 ?
You wouldn't have the table in front of you so you can't find the position of the number in the table

Actually if you can do this you would be sort of a human mini calculator, still far below Shakuntla Devi , a poor woman from India.



Memorize this table
1 1
2 8
3 27
4 64
5 125
6 216
7 343
8 512
9 729
10 1,000





The first digit of the square root can easily be calculated by looking at the up to 3 digit number before the comma (if any exists)
0 1 2 3 4 5 6 7 8 9
1 1,331 9,261 29,791 68,921 132,651 226,981 357,911 531,441 753,571
8 1,728 10,648 32,768 74,088 140,608 238,328 373,248 551,368 778,688
27 2,197 12,167 35,937 79,507 148,877 250,047 389,017 571,787 804,357
64 2,744 13,824 39,304 85,184 157,464 262,144 405,224 592,704 830,584
125 3,375 15,625 42,875 91,125 166,375 274,625 421,875 614,125 857,375
216 4,096 17,576 46,656 97,336 175,616 287,496 438,976 636,056 884,736
343 4,913 19,683 50,653 103,823 185,193 300,763 456,533 658,503 912,673
512 5,832 21,952 54,872 110,592 195,112 314,432 474,552 681,472 941,192
729 6,859 24,389 59,319 117,649 205,379 328,509 493,039 704,969 970,299
1,000 8,000 27,000 64,000 125,000 216,000 343,000 512,000 729,000 1,000,000




Look at final digit in table memorized in step 1

1 1
2 8
3 27
4 64
5 125
6 216
7 343
8 512
9 729
10 1000



Now try it again. What is the cube root of 148,877 ?

What have you got to lose?
November 30th, 2018 at 3:12:57 AM permalink
odiousgambit
Member since: Oct 28, 2012
Threads: 94
Posts: 2356
to solve the 23rd root, she would have been presented with :

916748676920039158098660927585380162483106680144308622407126516427934657040867096593279205767480806790022783016354924852380335745316935111903596577547340075681688305620821016129132845564805780158806771

she was better than my online calculator, which uses logarithms I assume. It came up with 546372890.9999996 as the answer , assuming that the above number is what was given to her

Holy cow!*

*no kidding, it just occurred to me that to say 'holy cow' might be very offensive to such a person, if she is Hindu. Is it possible that I summoned that up unconsciously? sorry for hijacking but I just had to ponder that
Mustard:You like Kipling, Miss Scarlet? Sure, I'll eat anything [from movie]
November 30th, 2018 at 6:12:28 AM permalink
Pacomartin
Member since: Oct 24, 2012
Threads: 869
Posts: 10320
Quote: odiousgambit
she was better than my online calculator, which uses logarithms I assume.


Yes, all calculators use logarithms to base 2.

In 1988 Shakuntala did the cube root of 95,443,993 in 2 seconds. She died in 2013 and received a Google Doodle.


450 91,125,000
451 91,733,851
452 92,345,408
453 92,959,677
454 93,576,664
455 94,196,375
456 94,818,816
457 95,443,993 ----------------------
458 96,071,912
459 96,702,579

It is actually possible for a normal person to do the cube roots of perfect cubes up to a million in 2 seconds, although you may want to draw it out as party trick.